dirichlet_hdg_post_rt.cc

The Poisson problem by the hybrid discontinuous Galerkin method – post-treatment with the Raviart-Thomas element

#include "rheolef.h"
using namespace rheolef;
using namespace std;
int main(int argc, char**argv) {
environment rheolef (argc, argv);
Float n, beta;
field sigma_h, uh, lambda_h;
din >> catchmark("n") >> n
>> catchmark("beta") >> beta
>> catchmark("u") >> uh
>> catchmark("lambda") >> lambda_h
>> catchmark("sigma") >> sigma_h;
const geo& omega = uh.get_geo();
size_t d = omega.dimension();
size_t k = uh.get_space().degree();
string approx = (k == 0) ? "empty" : "P"+itos(k-1)+"d";
space Tht(omega, "RT"+itos(k)+"d");
space Wht(omega, approx, "vector");
space Mht(omega, "trace(P"+itos(k)+"d)");
space Sht = Wht*Mht;
trial sigma_t (Tht); test tau (Sht);
auto tau_internal = tau[0], tau_n = tau[1];
auto coef = beta*pow(h_local(),n);
form aht = integrate (dot(sigma_t, tau_internal)
+ on_local_sides (dot(sigma_t,normal())*tau_n));
field lht = integrate(dot(sigma_h, tau_internal)
+ on_local_sides((dot(sigma_h,normal())
+ coef*(lambda_h - uh))*tau_n));
field sigma_ht (Tht);
problem p (aht);
p.solve (lht, sigma_ht);
dout << catchmark("n") << n << endl
<< catchmark("beta") << beta << endl
<< catchmark("u") << uh
<< catchmark("lambda") << lambda_h
<< catchmark("sigma") << sigma_h
<< catchmark("sigmat") << sigma_ht;
}
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::din
idiststream din
see the diststream page for the full documentation
Definition: diststream.h:427
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
main
int main(int argc, char **argv)
Definition: dirichlet_hdg_post_rt.cc:28
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_ball.n
int n
Definition: mkgeo_ball.sh:150
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::h_local
details::field_expr_v2_nonlinear_terminal_function< details::h_local_pseudo_function< Float > > h_local()
h_local: see the expression page for the full documentation
Definition: field_expr_terminal.h:527
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::on_local_sides
std::enable_if< details::is_field_expr_v2_variational_arg< Expr >::value,details::field_expr_quadrature_on_sides< Expr > >::type on_local_sides(const Expr &expr)
on_local_sides(expr): see the expression page for the full documentation
Definition: field_expr_quadrature.h:321
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::itos
std::string itos(std::string::size_type i)
itos: see the rheostream page for the full documentation
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25